According to OSHA, you have a right to refuse unsafe work. However, as @MisterPositive suggested, you can (and should according to the regulation) absolutely ask your employer for the right tools. This is part of your duty to:
Ask your employer to correct the hazard, or to assign other work.
You are not given the right tools (gloves, dust mask, etc).
You probably need to look at OSHA Regulations. The issue isn't that it's unrelated to your job description, it's that it's a safety hazard. There's contact information on their site you can use to ask questions and find out what your rights are.
You are asked to remove floor tile from an office.
Can you refuse this task?
Yes you can.
You can also most likely be terminated too. Take a look at your employment contract, employee handbook, etc. Most companies have this little clause "and other duties as necessary" that is designed to be a catch all for other miscellaneous crap the company may need you to do.
You might want to check with your ...